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<div class="title">opennurbs_knot.h</div>  </div>
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<div class="contents">
<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">/* $NoKeywords: $ */</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="comment">/*</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment">// Copyright (c) 1993-2012 Robert McNeel &amp; Associates. All rights reserved.</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment">// OpenNURBS, Rhinoceros, and Rhino3D are registered trademarks of Robert</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment">// McNeel &amp; Associates.</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment">// THIS SOFTWARE IS PROVIDED &quot;AS IS&quot; WITHOUT EXPRESS OR IMPLIED WARRANTY.</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="comment">// ALL IMPLIED WARRANTIES OF FITNESS FOR ANY PARTICULAR PURPOSE AND OF</span></div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;<span class="comment">// MERCHANTABILITY ARE HEREBY DISCLAIMED.</span></div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="comment">//              </span></div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;<span class="comment">// For complete openNURBS copyright information see &lt;http://www.opennurbs.org&gt;.</span></div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="comment">*/</span></div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160; </div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;<span class="preprocessor">#if !defined(OPENNURBS_KNOT_INC_)</span></div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;<span class="preprocessor">#define OPENNURBS_KNOT_INC_</span></div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160; </div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;ON_DECL</div>
<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;<span class="keywordtype">double</span> ON_DomainTolerance(</div>
<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;          <span class="keywordtype">double</span>, <span class="comment">// start of domain</span></div>
<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;          <span class="keywordtype">double</span>  <span class="comment">// end of domain</span></div>
<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;          );</div>
<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160; </div>
<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;ON_DECL</div>
<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;<span class="keywordtype">double</span> ON_KnotTolerance(</div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;          <span class="keywordtype">int</span>,           <span class="comment">// order (&gt;=2)</span></div>
<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;          <span class="keywordtype">int</span>,           <span class="comment">// cv count</span></div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;          <span class="keyword">const</span> <span class="keywordtype">double</span>*, <span class="comment">// knot[] array</span></div>
<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;          <span class="keywordtype">int</span>            <span class="comment">// knot index</span></div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;          );</div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160; </div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;ON_DECL</div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;<span class="keywordtype">double</span> ON_SpanTolerance(</div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;          <span class="keywordtype">int</span>,           <span class="comment">// order (&gt;=2)</span></div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;          <span class="keywordtype">int</span>,           <span class="comment">// cv count</span></div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;          <span class="keyword">const</span> <span class="keywordtype">double</span>*, <span class="comment">// knot[] array</span></div>
<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;          <span class="keywordtype">int</span>            <span class="comment">// span index</span></div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;          );</div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160; </div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;ON_DECL</div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;<span class="keywordtype">int</span> ON_KnotCount( <span class="comment">// returns (order + cv_count - 2)</span></div>
<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;          <span class="keywordtype">int</span>, <span class="comment">// order (&gt;=2)</span></div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;          <span class="keywordtype">int</span>  <span class="comment">// cv_count (&gt;=order)</span></div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;          );</div>
<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160; </div>
<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;ON_DECL</div>
<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;<span class="keywordtype">int</span> ON_KnotMultiplicity(</div>
<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;          <span class="keywordtype">int</span>,   <span class="comment">// order (&gt;=2)</span></div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;          <span class="keywordtype">int</span>,   <span class="comment">// cv_count (&gt;=order)</span></div>
<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;          <span class="keyword">const</span> <span class="keywordtype">double</span>*, <span class="comment">// knot[]</span></div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;          <span class="keywordtype">int</span>            <span class="comment">// knot_index</span></div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;          );</div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160; </div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;ON_DECL</div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;<span class="keywordtype">int</span> ON_KnotVectorSpanCount(</div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;          <span class="keywordtype">int</span>,           <span class="comment">// order (&gt;=2)</span></div>
<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;          <span class="keywordtype">int</span>,           <span class="comment">// cv count</span></div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;          <span class="keyword">const</span> <span class="keywordtype">double</span>*  <span class="comment">// knot[] array</span></div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;          );</div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160; </div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;ON_DECL</div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;<span class="keywordtype">bool</span> ON_GetKnotVectorSpanVector(</div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;          <span class="keywordtype">int</span>,           <span class="comment">// order (&gt;=2)</span></div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;          <span class="keywordtype">int</span>,           <span class="comment">// cv count</span></div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;          <span class="keyword">const</span> <span class="keywordtype">double</span>*, <span class="comment">// knot[] array</span></div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;          <span class="keywordtype">double</span>*        <span class="comment">// s[] array</span></div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;          );</div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160; </div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;<span class="comment">/*</span></div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;<span class="comment">Description:</span></div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;<span class="comment">  Given an evaluation parameter t in the domain of a NURBS curve,</span></div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;<span class="comment">  ON_NurbsSpanIndex(order,cv_count,knot,t,0,0) returns the integer</span></div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;<span class="comment">  i such that (knot[i],...,knot[i+2*degree-1]),  and </span></div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;<span class="comment">  (cv[i],...,cv[i+degree]) are the knots and control points that</span></div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;<span class="comment">  define the span of the NURBS that are used for evaluation at t.</span></div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;<span class="comment">Parameters:</span></div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;<span class="comment">  order - [in] order &gt;= 2</span></div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;<span class="comment">  cv_count - [in] cv_count &gt;= order</span></div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;<span class="comment">  knot - [in] valid knot vector</span></div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;<span class="comment">  t - [in] evaluation parameter</span></div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;<span class="comment">  side - [in] determines which span is used when t is at a knot</span></div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;<span class="comment">              value;  side = 0 for the default (from above),</span></div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;<span class="comment">              side = -1 means from below, and </span></div>
<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;<span class="comment">              side = +1 means from above.</span></div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;<span class="comment">  hint - [in] Search hint, or 0 if not hint is available.</span></div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;<span class="comment">Returns:</span></div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;<span class="comment">  Returns the index described above.</span></div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;<span class="comment">*/</span></div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;ON_DECL</div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;<span class="keywordtype">int</span> ON_NurbsSpanIndex(</div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;          <span class="keywordtype">int</span> order,</div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;          <span class="keywordtype">int</span> cv_count,</div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;          <span class="keyword">const</span> <span class="keywordtype">double</span>* knot,</div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;          <span class="keywordtype">double</span> t,</div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;          <span class="keywordtype">int</span> side,</div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;          <span class="keywordtype">int</span> hint</div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;          );</div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160; </div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;ON_DECL</div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;<span class="keywordtype">int</span> ON_NextNurbsSpanIndex(</div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;          <span class="comment">// returns  0: input span_index &lt; 0</span></div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;          <span class="comment">//           cv_count-order: input span_index = cv_count-order</span></div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;          <span class="comment">//         -1: input span_index &gt; cv_count-order;</span></div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;          <span class="comment">//     otherwise next span index</span></div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;          <span class="keywordtype">int</span> order,</div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;          <span class="keywordtype">int</span> cv_count,</div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;          <span class="keyword">const</span> <span class="keywordtype">double</span>* knot,</div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;          <span class="keywordtype">int</span>            <span class="comment">// current span_index </span></div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;          );</div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160; </div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;ON_DECL</div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;<span class="keywordtype">int</span> ON_GetSpanIndices( <span class="comment">// returns span count, which is one less than length of span_indices[]</span></div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;          <span class="keywordtype">int</span> order,</div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;          <span class="keywordtype">int</span> cv_count,</div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;          <span class="keyword">const</span> <span class="keywordtype">double</span>* knot,</div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;          <span class="keywordtype">int</span>*           <span class="comment">// span_indices[cv_count-order+2]. </span></div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;                         <span class="comment">//Indices of knots at end of group of mult knots </span></div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;                         <span class="comment">//at start of span, and knot at start of group of mult knots</span></div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;                         <span class="comment">//at end of spline.</span></div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;          );</div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160; </div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;ON_DECL</div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;<span class="keywordtype">double</span> ON_SuperfluousKnot( </div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;          <span class="keywordtype">int</span> order,</div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;          <span class="keywordtype">int</span> cv_count,</div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;          <span class="keyword">const</span> <span class="keywordtype">double</span>* knot,</div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;          <span class="keywordtype">int</span>            <span class="comment">// 0 = first superfluous knot </span></div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;                         <span class="comment">// 1 = last superfluous knot</span></div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;          );</div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160; </div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;ON_DECL</div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;<span class="keywordtype">bool</span> ON_IsKnotVectorPeriodic(</div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;          <span class="keywordtype">int</span> order,</div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;          <span class="keywordtype">int</span> cv_count,</div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;          <span class="keyword">const</span> <span class="keywordtype">double</span>* knot</div>
<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;          );</div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160; </div>
<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;ON_DECL</div>
<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;<span class="keywordtype">bool</span> ON_IsKnotVectorClamped(</div>
<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;          <span class="keywordtype">int</span> order,</div>
<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;          <span class="keywordtype">int</span> cv_count,</div>
<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;          <span class="keyword">const</span> <span class="keywordtype">double</span>* knot,</div>
<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;          <span class="keywordtype">int</span> = 2        <span class="comment">// 0 = check left end, 1 = check right end, 2 = check both</span></div>
<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;          );</div>
<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160; </div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;ON_DECL</div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;<span class="keywordtype">bool</span> ON_IsKnotVectorUniform(</div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;          <span class="keywordtype">int</span> order,</div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;          <span class="keywordtype">int</span> cv_count,</div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;          <span class="keyword">const</span> <span class="keywordtype">double</span>* knot </div>
<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;          );</div>
<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160; </div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;<span class="comment">// returns true if all knots have multiplicity = degree</span></div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;ON_DECL</div>
<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;<span class="keywordtype">bool</span> ON_KnotVectorHasBezierSpans(</div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;          <span class="keywordtype">int</span> order,</div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;          <span class="keywordtype">int</span> cv_count,</div>
<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;          <span class="keyword">const</span> <span class="keywordtype">double</span>* knot</div>
<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;          );</div>
<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160; </div>
<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160; </div>
<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;ON_DECL</div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;ON::knot_style ON_KnotVectorStyle( </div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;          <span class="keywordtype">int</span> order,</div>
<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;          <span class="keywordtype">int</span> cv_count,</div>
<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;          <span class="keyword">const</span> <span class="keywordtype">double</span>* knot</div>
<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;          );</div>
<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160; </div>
<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;<span class="comment">/*</span></div>
<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;<span class="comment">Description:</span></div>
<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;<span class="comment">  Set the domain of a knot vector.</span></div>
<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;<span class="comment">Parameters:</span></div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;<span class="comment">  order - [in] order &gt;= 2</span></div>
<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;<span class="comment">  cv_count - [in] cv_count &gt;= order</span></div>
<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;<span class="comment">  knot - [in/out] input existing knots and returns knots with new domain.</span></div>
<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;<span class="comment">  t0 - [in]</span></div>
<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;<span class="comment">  t1 - [in] New domain will be the interval (t0,t1).</span></div>
<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;<span class="comment">Returns:</span></div>
<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;<span class="comment">  True if input is valid and the returned knot vector </span></div>
<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;<span class="comment">  has the requested domain.  False if the input is</span></div>
<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;<span class="comment">  invalid, in which case the input knot vector is not</span></div>
<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;<span class="comment">  changed.</span></div>
<div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160;<span class="comment">*/</span></div>
<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;ON_DECL</div>
<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;<span class="keywordtype">bool</span> ON_SetKnotVectorDomain( </div>
<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;          <span class="keywordtype">int</span> order, </div>
<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;          <span class="keywordtype">int</span> cv_count, </div>
<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;          <span class="keywordtype">double</span>* knot, </div>
<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;          <span class="keywordtype">double</span> t0, </div>
<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;          <span class="keywordtype">double</span> t1 </div>
<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;          );</div>
<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160; </div>
<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;ON_DECL</div>
<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;<span class="keywordtype">bool</span> ON_GetKnotVectorDomain(</div>
<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;          <span class="keywordtype">int</span>,           <span class="comment">// order (&gt;=2)</span></div>
<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;          <span class="keywordtype">int</span>,           <span class="comment">// cv count</span></div>
<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;          <span class="keyword">const</span> <span class="keywordtype">double</span>*, <span class="comment">// knot[] array</span></div>
<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;          <span class="keywordtype">double</span>*, <span class="keywordtype">double</span>*</div>
<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;          );</div>
<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160; </div>
<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;ON_DECL</div>
<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;<span class="keywordtype">bool</span> ON_ReverseKnotVector(</div>
<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;          <span class="keywordtype">int</span>,           <span class="comment">// order (&gt;=2)</span></div>
<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;          <span class="keywordtype">int</span>,           <span class="comment">// cv count</span></div>
<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;          <span class="keywordtype">double</span>*        <span class="comment">// knot[] array</span></div>
<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;          );</div>
<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160; </div>
<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;ON_DECL</div>
<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;<span class="keywordtype">int</span> ON_CompareKnotVector( <span class="comment">// returns </span></div>
<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;                                      <span class="comment">// -1: first &lt; second</span></div>
<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;                                      <span class="comment">//  0: first == second</span></div>
<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;                                      <span class="comment">// +1: first &gt; second</span></div>
<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;          <span class="comment">// first knot vector</span></div>
<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;          <span class="keywordtype">int</span>,           <span class="comment">// order (&gt;=2)</span></div>
<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;          <span class="keywordtype">int</span>,           <span class="comment">// cv count</span></div>
<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;          <span class="keyword">const</span> <span class="keywordtype">double</span>*, <span class="comment">// knot[] array</span></div>
<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;          <span class="comment">// second knot vector</span></div>
<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;          <span class="keywordtype">int</span>,           <span class="comment">// order (&gt;=2)</span></div>
<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;          <span class="keywordtype">int</span>,           <span class="comment">// cv count</span></div>
<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;          <span class="keyword">const</span> <span class="keywordtype">double</span>*  <span class="comment">// knot[] array</span></div>
<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;          );</div>
<div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160; </div>
<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;ON_DECL</div>
<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;<span class="keywordtype">bool</span> ON_IsValidKnotVector(</div>
<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160;          <span class="keywordtype">int</span> order,</div>
<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;          <span class="keywordtype">int</span> cv_count, </div>
<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;          <span class="keyword">const</span> <span class="keywordtype">double</span>* knot, </div>
<div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160;          <a class="code" href="class_o_n___text_log.html">ON_TextLog</a>* text_log = 0</div>
<div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160;          );</div>
<div class="line"><a name="l00233"></a><span class="lineno">  233</span>&#160; </div>
<div class="line"><a name="l00234"></a><span class="lineno">  234</span>&#160;ON_DECL</div>
<div class="line"><a name="l00235"></a><span class="lineno">  235</span>&#160;<span class="keywordtype">bool</span> ON_ClampKnotVector(</div>
<div class="line"><a name="l00236"></a><span class="lineno">  236</span>&#160;          <span class="comment">// Sets inital/final order-2 knots to values in</span></div>
<div class="line"><a name="l00237"></a><span class="lineno">  237</span>&#160;          <span class="comment">// knot[order-2]/knot[cv_count-1].</span></div>
<div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160;          <span class="keywordtype">int</span>,           <span class="comment">// order (&gt;=2)</span></div>
<div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;          <span class="keywordtype">int</span>,           <span class="comment">// cv count</span></div>
<div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160;          <span class="keywordtype">double</span>*,       <span class="comment">// knot[] array</span></div>
<div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160;          <span class="keywordtype">int</span>            <span class="comment">// 0 = clamp left end, 1 = right end, 2 = clamp both ends</span></div>
<div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;          );</div>
<div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160; </div>
<div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160;ON_DECL</div>
<div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160;<span class="keywordtype">bool</span> ON_MakeKnotVectorPeriodic(</div>
<div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160;          <span class="comment">// Sets inital and final order-2 knots to values</span></div>
<div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;          <span class="comment">// that make the knot vector periodic</span></div>
<div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160;          <span class="keywordtype">int</span>,           <span class="comment">// order (&gt;=2)</span></div>
<div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160;          <span class="keywordtype">int</span>,           <span class="comment">// cv count</span></div>
<div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;          <span class="keywordtype">double</span>*        <span class="comment">// knot[] array</span></div>
<div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160;          );</div>
<div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160; </div>
<div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160; <span class="comment">/*</span></div>
<div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160;<span class="comment"> Description:</span></div>
<div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;<span class="comment">   Fill in knot values for a clamped uniform knot</span></div>
<div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160;<span class="comment">   vector.</span></div>
<div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160;<span class="comment"> Parameters:</span></div>
<div class="line"><a name="l00258"></a><span class="lineno">  258</span>&#160;<span class="comment">   order - [in] (&gt;=2) order (degree+1) of the NURBS</span></div>
<div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160;<span class="comment">   cv_count - [in] (&gt;=order) total number of control points</span></div>
<div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160;<span class="comment">       in the NURBS.</span></div>
<div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160;<span class="comment">   knot - [in/out] Input is an array with room for </span></div>
<div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160;<span class="comment">       ON_KnotCount(order,cv_count) doubles.  Output is</span></div>
<div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160;<span class="comment">       a clamped uniform knot vector with domain</span></div>
<div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160;<span class="comment">       (0, (1+cv_count-order)*delta).</span></div>
<div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160;<span class="comment">   delta - [in] (&gt;0, default=1.0) spacing between knots.</span></div>
<div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;<span class="comment"> Returns:</span></div>
<div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160;<span class="comment">   true if successful</span></div>
<div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160;<span class="comment"> See Also:</span></div>
<div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160;<span class="comment">   ON_NurbsCurve::MakeClampedUniformKnotVector</span></div>
<div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160;<span class="comment">*/</span></div>
<div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160;ON_DECL</div>
<div class="line"><a name="l00272"></a><span class="lineno">  272</span>&#160;<span class="keywordtype">bool</span> ON_MakeClampedUniformKnotVector(</div>
<div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160;          <span class="keywordtype">int</span> order,</div>
<div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160;          <span class="keywordtype">int</span> cv_count,</div>
<div class="line"><a name="l00275"></a><span class="lineno">  275</span>&#160;          <span class="keywordtype">double</span>* knot,</div>
<div class="line"><a name="l00276"></a><span class="lineno">  276</span>&#160;          <span class="keywordtype">double</span> delta = 1.0</div>
<div class="line"><a name="l00277"></a><span class="lineno">  277</span>&#160;          );</div>
<div class="line"><a name="l00278"></a><span class="lineno">  278</span>&#160; </div>
<div class="line"><a name="l00279"></a><span class="lineno">  279</span>&#160;<span class="comment">/*</span></div>
<div class="line"><a name="l00280"></a><span class="lineno">  280</span>&#160;<span class="comment"> Description:</span></div>
<div class="line"><a name="l00281"></a><span class="lineno">  281</span>&#160;<span class="comment">   Fill in knot values for a clamped uniform knot</span></div>
<div class="line"><a name="l00282"></a><span class="lineno">  282</span>&#160;<span class="comment">   vector.</span></div>
<div class="line"><a name="l00283"></a><span class="lineno">  283</span>&#160;<span class="comment"> Parameters:</span></div>
<div class="line"><a name="l00284"></a><span class="lineno">  284</span>&#160;<span class="comment">   order - [in] (&gt;=2) order (degree+1) of the NURBS</span></div>
<div class="line"><a name="l00285"></a><span class="lineno">  285</span>&#160;<span class="comment">   cv_count - [in] (&gt;=order) total number of control points</span></div>
<div class="line"><a name="l00286"></a><span class="lineno">  286</span>&#160;<span class="comment">       in the NURBS.</span></div>
<div class="line"><a name="l00287"></a><span class="lineno">  287</span>&#160;<span class="comment">   knot - [in/out] Input is an array with room for </span></div>
<div class="line"><a name="l00288"></a><span class="lineno">  288</span>&#160;<span class="comment">       ON_KnotCount(order,cv_count) doubles.  Output is</span></div>
<div class="line"><a name="l00289"></a><span class="lineno">  289</span>&#160;<span class="comment">       a periodic uniform knot vector with domain</span></div>
<div class="line"><a name="l00290"></a><span class="lineno">  290</span>&#160;<span class="comment">       (0, (1+cv_count-order)*delta).</span></div>
<div class="line"><a name="l00291"></a><span class="lineno">  291</span>&#160;<span class="comment">   delta - [in] (&gt;0, default=1.0) spacing between knots.</span></div>
<div class="line"><a name="l00292"></a><span class="lineno">  292</span>&#160;<span class="comment"> Returns:</span></div>
<div class="line"><a name="l00293"></a><span class="lineno">  293</span>&#160;<span class="comment">   true if successful</span></div>
<div class="line"><a name="l00294"></a><span class="lineno">  294</span>&#160;<span class="comment"> See Also:</span></div>
<div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160;<span class="comment">   ON_NurbsCurve::MakePeriodicUniformKnotVector</span></div>
<div class="line"><a name="l00296"></a><span class="lineno">  296</span>&#160;<span class="comment">*/</span></div>
<div class="line"><a name="l00297"></a><span class="lineno">  297</span>&#160;ON_DECL</div>
<div class="line"><a name="l00298"></a><span class="lineno">  298</span>&#160;<span class="keywordtype">bool</span> ON_MakePeriodicUniformKnotVector(</div>
<div class="line"><a name="l00299"></a><span class="lineno">  299</span>&#160;          <span class="keywordtype">int</span> order,</div>
<div class="line"><a name="l00300"></a><span class="lineno">  300</span>&#160;          <span class="keywordtype">int</span> cv_count,</div>
<div class="line"><a name="l00301"></a><span class="lineno">  301</span>&#160;          <span class="keywordtype">double</span>* knot,</div>
<div class="line"><a name="l00302"></a><span class="lineno">  302</span>&#160;          <span class="keywordtype">double</span> delta = 1.0</div>
<div class="line"><a name="l00303"></a><span class="lineno">  303</span>&#160;          );</div>
<div class="line"><a name="l00304"></a><span class="lineno">  304</span>&#160; </div>
<div class="line"><a name="l00305"></a><span class="lineno">  305</span>&#160;ON_DECL</div>
<div class="line"><a name="l00306"></a><span class="lineno">  306</span>&#160;<span class="keywordtype">double</span> ON_GrevilleAbcissa( <span class="comment">// get Greville abcissae from knots</span></div>
<div class="line"><a name="l00307"></a><span class="lineno">  307</span>&#160;          <span class="keywordtype">int</span>,           <span class="comment">// order (&gt;=2)</span></div>
<div class="line"><a name="l00308"></a><span class="lineno">  308</span>&#160;          <span class="keyword">const</span> <span class="keywordtype">double</span>*  <span class="comment">// knot[] array (length = order-1)</span></div>
<div class="line"><a name="l00309"></a><span class="lineno">  309</span>&#160;          );</div>
<div class="line"><a name="l00310"></a><span class="lineno">  310</span>&#160; </div>
<div class="line"><a name="l00311"></a><span class="lineno">  311</span>&#160;ON_DECL</div>
<div class="line"><a name="l00312"></a><span class="lineno">  312</span>&#160;<span class="keywordtype">bool</span> ON_GetGrevilleAbcissae( <span class="comment">// get Greville abcissae from knots</span></div>
<div class="line"><a name="l00313"></a><span class="lineno">  313</span>&#160;          <span class="keywordtype">int</span>,            <span class="comment">// order (&gt;=2)</span></div>
<div class="line"><a name="l00314"></a><span class="lineno">  314</span>&#160;          <span class="keywordtype">int</span>,            <span class="comment">// cv count</span></div>
<div class="line"><a name="l00315"></a><span class="lineno">  315</span>&#160;          <span class="keyword">const</span> <span class="keywordtype">double</span>*,  <span class="comment">// knot[] array</span></div>
<div class="line"><a name="l00316"></a><span class="lineno">  316</span>&#160;          <span class="keywordtype">bool</span>,           <span class="comment">// true for periodic case</span></div>
<div class="line"><a name="l00317"></a><span class="lineno">  317</span>&#160;          <span class="keywordtype">double</span>*         <span class="comment">// g[] array has length cv_count in non-periodic case</span></div>
<div class="line"><a name="l00318"></a><span class="lineno">  318</span>&#160;                          <span class="comment">// and cv_count-order+1 in periodic case</span></div>
<div class="line"><a name="l00319"></a><span class="lineno">  319</span>&#160;          );</div>
<div class="line"><a name="l00320"></a><span class="lineno">  320</span>&#160; </div>
<div class="line"><a name="l00321"></a><span class="lineno">  321</span>&#160;ON_DECL</div>
<div class="line"><a name="l00322"></a><span class="lineno">  322</span>&#160;<span class="keywordtype">bool</span> ON_GetGrevilleKnotVector( <span class="comment">// get knots from Greville abcissa</span></div>
<div class="line"><a name="l00323"></a><span class="lineno">  323</span>&#160;          <span class="keywordtype">int</span>,           <span class="comment">// g[] array stride (&gt;=1)</span></div>
<div class="line"><a name="l00324"></a><span class="lineno">  324</span>&#160;          <span class="keyword">const</span> <span class="keywordtype">double</span>*, <span class="comment">// g[] array</span></div>
<div class="line"><a name="l00325"></a><span class="lineno">  325</span>&#160;                         <span class="comment">// if not periodic, length = cv_count</span></div>
<div class="line"><a name="l00326"></a><span class="lineno">  326</span>&#160;                         <span class="comment">// if periodic, length = cv_count-order+2</span></div>
<div class="line"><a name="l00327"></a><span class="lineno">  327</span>&#160;          <span class="keywordtype">bool</span>,          <span class="comment">// true for periodic knots</span></div>
<div class="line"><a name="l00328"></a><span class="lineno">  328</span>&#160;          <span class="keywordtype">int</span>,           <span class="comment">// order (&gt;=2)</span></div>
<div class="line"><a name="l00329"></a><span class="lineno">  329</span>&#160;          <span class="keywordtype">int</span>,           <span class="comment">// cv_count (&gt;=order)</span></div>
<div class="line"><a name="l00330"></a><span class="lineno">  330</span>&#160;          <span class="keywordtype">double</span>*        <span class="comment">// knot[cv_count+order-2]</span></div>
<div class="line"><a name="l00331"></a><span class="lineno">  331</span>&#160;          );</div>
<div class="line"><a name="l00332"></a><span class="lineno">  332</span>&#160; </div>
<div class="line"><a name="l00333"></a><span class="lineno">  333</span>&#160;ON_DECL</div>
<div class="line"><a name="l00334"></a><span class="lineno">  334</span>&#160;<span class="keywordtype">bool</span> ON_ClampKnotVector(</div>
<div class="line"><a name="l00335"></a><span class="lineno">  335</span>&#160;        <span class="keywordtype">int</span>,       <span class="comment">// cv_dim ( = dim+1 for rational cvs )</span></div>
<div class="line"><a name="l00336"></a><span class="lineno">  336</span>&#160;        <span class="keywordtype">int</span>,       <span class="comment">// order (&gt;=2)</span></div>
<div class="line"><a name="l00337"></a><span class="lineno">  337</span>&#160;        <span class="keywordtype">int</span>,       <span class="comment">// cv_count,</span></div>
<div class="line"><a name="l00338"></a><span class="lineno">  338</span>&#160;        <span class="keywordtype">int</span>,       <span class="comment">// cv_stride, </span></div>
<div class="line"><a name="l00339"></a><span class="lineno">  339</span>&#160;        <span class="keywordtype">double</span>*,   <span class="comment">// cv[] NULL or array of order many cvs</span></div>
<div class="line"><a name="l00340"></a><span class="lineno">  340</span>&#160;        <span class="keywordtype">double</span>*,   <span class="comment">// knot[] array with room for at least knot_multiplicity new knots</span></div>
<div class="line"><a name="l00341"></a><span class="lineno">  341</span>&#160;        <span class="keywordtype">int</span>        <span class="comment">// end  0 = clamp start, 1 = clamp end, 2 = clamp both ends</span></div>
<div class="line"><a name="l00342"></a><span class="lineno">  342</span>&#160;        );</div>
<div class="line"><a name="l00343"></a><span class="lineno">  343</span>&#160; </div>
<div class="line"><a name="l00344"></a><span class="lineno">  344</span>&#160;<span class="comment">/*</span></div>
<div class="line"><a name="l00345"></a><span class="lineno">  345</span>&#160;<span class="comment">Returns:</span></div>
<div class="line"><a name="l00346"></a><span class="lineno">  346</span>&#160;<span class="comment">  Number of knots added.</span></div>
<div class="line"><a name="l00347"></a><span class="lineno">  347</span>&#160;<span class="comment">*/</span></div>
<div class="line"><a name="l00348"></a><span class="lineno">  348</span>&#160;ON_DECL</div>
<div class="line"><a name="l00349"></a><span class="lineno">  349</span>&#160;<span class="keywordtype">int</span> ON_InsertKnot(</div>
<div class="line"><a name="l00350"></a><span class="lineno">  350</span>&#160;        <span class="keywordtype">double</span>,    <span class="comment">// knot_value,</span></div>
<div class="line"><a name="l00351"></a><span class="lineno">  351</span>&#160;        <span class="keywordtype">int</span>,       <span class="comment">// knot_multiplicity, (1 to order-1 including multiplicity of any existing knots)</span></div>
<div class="line"><a name="l00352"></a><span class="lineno">  352</span>&#160;        <span class="keywordtype">int</span>,       <span class="comment">// cv_dim ( = dim+1 for rational cvs )</span></div>
<div class="line"><a name="l00353"></a><span class="lineno">  353</span>&#160;        <span class="keywordtype">int</span>,       <span class="comment">// order (&gt;=2)</span></div>
<div class="line"><a name="l00354"></a><span class="lineno">  354</span>&#160;        <span class="keywordtype">int</span>,       <span class="comment">// cv_count,</span></div>
<div class="line"><a name="l00355"></a><span class="lineno">  355</span>&#160;        <span class="keywordtype">int</span>,       <span class="comment">// cv_stride (&gt;=cv_dim)</span></div>
<div class="line"><a name="l00356"></a><span class="lineno">  356</span>&#160;        <span class="keywordtype">double</span>*,   <span class="comment">// cv[]  NULL or cv array with room for at least knot_multiplicity new cvs</span></div>
<div class="line"><a name="l00357"></a><span class="lineno">  357</span>&#160;        <span class="keywordtype">double</span>*,   <span class="comment">// knot[] knot array with room for at least knot_multiplicity new knots</span></div>
<div class="line"><a name="l00358"></a><span class="lineno">  358</span>&#160;        <span class="keywordtype">int</span>*       <span class="comment">// hint, optional hint about where to search for span to add knots to</span></div>
<div class="line"><a name="l00359"></a><span class="lineno">  359</span>&#160;                   <span class="comment">// pass NULL if no hint is available</span></div>
<div class="line"><a name="l00360"></a><span class="lineno">  360</span>&#160;        );</div>
<div class="line"><a name="l00361"></a><span class="lineno">  361</span>&#160; </div>
<div class="line"><a name="l00362"></a><span class="lineno">  362</span>&#160;<span class="comment">/*</span></div>
<div class="line"><a name="l00363"></a><span class="lineno">  363</span>&#160;<span class="comment">Description:</span></div>
<div class="line"><a name="l00364"></a><span class="lineno">  364</span>&#160;<span class="comment">  Reparameterize a rational Bezier curve.</span></div>
<div class="line"><a name="l00365"></a><span class="lineno">  365</span>&#160;<span class="comment">Parameters:</span></div>
<div class="line"><a name="l00366"></a><span class="lineno">  366</span>&#160;<span class="comment">  c - [in]</span></div>
<div class="line"><a name="l00367"></a><span class="lineno">  367</span>&#160;<span class="comment">    reparameterization constant (generally speaking, c should be &gt; 0).</span></div>
<div class="line"><a name="l00368"></a><span class="lineno">  368</span>&#160;<span class="comment">    The control points are adjusted so that </span></div>
<div class="line"><a name="l00369"></a><span class="lineno">  369</span>&#160;<span class="comment">    output_bezier(t) = input_bezier(lambda(t)), where</span></div>
<div class="line"><a name="l00370"></a><span class="lineno">  370</span>&#160;<span class="comment">    lambda(t) = c*t/( (c-1)*t + 1 ).</span></div>
<div class="line"><a name="l00371"></a><span class="lineno">  371</span>&#160;<span class="comment">    Note that lambda(0) = 0, lambda(1) = 1, lambda&#39;(t) &gt; 0, </span></div>
<div class="line"><a name="l00372"></a><span class="lineno">  372</span>&#160;<span class="comment">    lambda&#39;(0) = c and lambda&#39;(1) = 1/c.</span></div>
<div class="line"><a name="l00373"></a><span class="lineno">  373</span>&#160;<span class="comment">  dim - [in]</span></div>
<div class="line"><a name="l00374"></a><span class="lineno">  374</span>&#160;<span class="comment">  order - [in]</span></div>
<div class="line"><a name="l00375"></a><span class="lineno">  375</span>&#160;<span class="comment">  cvstride - [in] (&gt;= dim+1)</span></div>
<div class="line"><a name="l00376"></a><span class="lineno">  376</span>&#160;<span class="comment">  cv - [in/out]  homogeneous rational control points</span></div>
<div class="line"><a name="l00377"></a><span class="lineno">  377</span>&#160;<span class="comment">Returns:</span></div>
<div class="line"><a name="l00378"></a><span class="lineno">  378</span>&#160;<span class="comment">  The cv values are changed so that</span></div>
<div class="line"><a name="l00379"></a><span class="lineno">  379</span>&#160;<span class="comment">  output_bezier(t) = input_bezier(lambda(t)).</span></div>
<div class="line"><a name="l00380"></a><span class="lineno">  380</span>&#160;<span class="comment">*/</span></div>
<div class="line"><a name="l00381"></a><span class="lineno">  381</span>&#160;ON_DECL</div>
<div class="line"><a name="l00382"></a><span class="lineno">  382</span>&#160;<span class="keywordtype">bool</span> ON_ReparameterizeRationalBezierCurve(</div>
<div class="line"><a name="l00383"></a><span class="lineno">  383</span>&#160;          <span class="keywordtype">double</span> c,</div>
<div class="line"><a name="l00384"></a><span class="lineno">  384</span>&#160;          <span class="keywordtype">int</span> dim,</div>
<div class="line"><a name="l00385"></a><span class="lineno">  385</span>&#160;          <span class="keywordtype">int</span> order,</div>
<div class="line"><a name="l00386"></a><span class="lineno">  386</span>&#160;          <span class="keywordtype">int</span> cvstride,</div>
<div class="line"><a name="l00387"></a><span class="lineno">  387</span>&#160;          <span class="keywordtype">double</span>* cv</div>
<div class="line"><a name="l00388"></a><span class="lineno">  388</span>&#160;          );</div>
<div class="line"><a name="l00389"></a><span class="lineno">  389</span>&#160; </div>
<div class="line"><a name="l00390"></a><span class="lineno">  390</span>&#160;<span class="comment">/*</span></div>
<div class="line"><a name="l00391"></a><span class="lineno">  391</span>&#160;<span class="comment">Description:</span></div>
<div class="line"><a name="l00392"></a><span class="lineno">  392</span>&#160;<span class="comment">  Use a combination of scaling and reparameterization to set two rational</span></div>
<div class="line"><a name="l00393"></a><span class="lineno">  393</span>&#160;<span class="comment">  Bezier weights to specified values.</span></div>
<div class="line"><a name="l00394"></a><span class="lineno">  394</span>&#160;<span class="comment">Parameters:</span></div>
<div class="line"><a name="l00395"></a><span class="lineno">  395</span>&#160;<span class="comment">  dim - [in] </span></div>
<div class="line"><a name="l00396"></a><span class="lineno">  396</span>&#160;<span class="comment">  order - [in]</span></div>
<div class="line"><a name="l00397"></a><span class="lineno">  397</span>&#160;<span class="comment">  cvstride - [in] ( &gt;= dim+1)</span></div>
<div class="line"><a name="l00398"></a><span class="lineno">  398</span>&#160;<span class="comment">  cv - [in/out]  homogeneous rational control points</span></div>
<div class="line"><a name="l00399"></a><span class="lineno">  399</span>&#160;<span class="comment">  i0 - [in] </span></div>
<div class="line"><a name="l00400"></a><span class="lineno">  400</span>&#160;<span class="comment">  w0 - [in]</span></div>
<div class="line"><a name="l00401"></a><span class="lineno">  401</span>&#160;<span class="comment">  i1 - [in]</span></div>
<div class="line"><a name="l00402"></a><span class="lineno">  402</span>&#160;<span class="comment">  w1 - [in]</span></div>
<div class="line"><a name="l00403"></a><span class="lineno">  403</span>&#160;<span class="comment">    The i0-th cv will have weight w0 and the i1-th cv will have weight w1.</span></div>
<div class="line"><a name="l00404"></a><span class="lineno">  404</span>&#160;<span class="comment">    If v0 and v1 are the cv&#39;s input weights, then v0, v1, w0 and w1 must</span></div>
<div class="line"><a name="l00405"></a><span class="lineno">  405</span>&#160;<span class="comment">    all be nonzero, and w0*v0 and w1*v1 must have the same sign.</span></div>
<div class="line"><a name="l00406"></a><span class="lineno">  406</span>&#160;<span class="comment">Returns:</span></div>
<div class="line"><a name="l00407"></a><span class="lineno">  407</span>&#160;<span class="comment">  true if successful</span></div>
<div class="line"><a name="l00408"></a><span class="lineno">  408</span>&#160;<span class="comment">Remarks:</span></div>
<div class="line"><a name="l00409"></a><span class="lineno">  409</span>&#160;<span class="comment">  The equations</span></div>
<div class="line"><a name="l00410"></a><span class="lineno">  410</span>&#160;<span class="comment">    s * r^i0 = w0/v0</span></div>
<div class="line"><a name="l00411"></a><span class="lineno">  411</span>&#160;<span class="comment">    s * r^i1 = w1/v1</span></div>
<div class="line"><a name="l00412"></a><span class="lineno">  412</span>&#160;<span class="comment">  determine the scaling and reparameterization necessary to change v0,v1 to</span></div>
<div class="line"><a name="l00413"></a><span class="lineno">  413</span>&#160;<span class="comment">  w0,w1. </span></div>
<div class="line"><a name="l00414"></a><span class="lineno">  414</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l00415"></a><span class="lineno">  415</span>&#160;<span class="comment">  If the input Bezier has control vertices {B_0, ..., B_d}, then the </span></div>
<div class="line"><a name="l00416"></a><span class="lineno">  416</span>&#160;<span class="comment">  output Bezier has control vertices {s*B_0, ... s*r^i * B_i, ..., s*r^d * B_d}.</span></div>
<div class="line"><a name="l00417"></a><span class="lineno">  417</span>&#160;<span class="comment">*/</span></div>
<div class="line"><a name="l00418"></a><span class="lineno">  418</span>&#160;ON_DECL</div>
<div class="line"><a name="l00419"></a><span class="lineno">  419</span>&#160;<span class="keywordtype">bool</span> ON_ChangeRationalBezierCurveWeights(</div>
<div class="line"><a name="l00420"></a><span class="lineno">  420</span>&#160;          <span class="keywordtype">int</span> dim, <span class="keywordtype">int</span> order, <span class="keywordtype">int</span> cvstride, <span class="keywordtype">double</span>* cv,</div>
<div class="line"><a name="l00421"></a><span class="lineno">  421</span>&#160;          <span class="keywordtype">int</span> i0, <span class="keywordtype">double</span> w0, </div>
<div class="line"><a name="l00422"></a><span class="lineno">  422</span>&#160;          <span class="keywordtype">int</span> i1, <span class="keywordtype">double</span> w1</div>
<div class="line"><a name="l00423"></a><span class="lineno">  423</span>&#160;          );</div>
<div class="line"><a name="l00424"></a><span class="lineno">  424</span>&#160; </div>
<div class="line"><a name="l00425"></a><span class="lineno">  425</span>&#160;<span class="comment">/*</span></div>
<div class="line"><a name="l00426"></a><span class="lineno">  426</span>&#160;<span class="comment">Description:</span></div>
<div class="line"><a name="l00427"></a><span class="lineno">  427</span>&#160;<span class="comment">  Reparameterize a rational NURBS curve.</span></div>
<div class="line"><a name="l00428"></a><span class="lineno">  428</span>&#160;<span class="comment">Parameters:</span></div>
<div class="line"><a name="l00429"></a><span class="lineno">  429</span>&#160;<span class="comment">  c - [in]</span></div>
<div class="line"><a name="l00430"></a><span class="lineno">  430</span>&#160;<span class="comment">    reparameterization constant (generally speaking, c should be &gt; 0).</span></div>
<div class="line"><a name="l00431"></a><span class="lineno">  431</span>&#160;<span class="comment">    The control points and knots are adjusted so that </span></div>
<div class="line"><a name="l00432"></a><span class="lineno">  432</span>&#160;<span class="comment">    output_nurbs(t) = input_nurbs(lambda(t)), where</span></div>
<div class="line"><a name="l00433"></a><span class="lineno">  433</span>&#160;<span class="comment">    lambda(t) = c*t/( (c-1)*t + 1 ).</span></div>
<div class="line"><a name="l00434"></a><span class="lineno">  434</span>&#160;<span class="comment">    Note that lambda(0) = 0, lambda(1) = 1, lambda&#39;(t) &gt; 0, </span></div>
<div class="line"><a name="l00435"></a><span class="lineno">  435</span>&#160;<span class="comment">    lambda&#39;(0) = c and lambda&#39;(1) = 1/c.</span></div>
<div class="line"><a name="l00436"></a><span class="lineno">  436</span>&#160;<span class="comment">  dim - [in]</span></div>
<div class="line"><a name="l00437"></a><span class="lineno">  437</span>&#160;<span class="comment">  order - [in]</span></div>
<div class="line"><a name="l00438"></a><span class="lineno">  438</span>&#160;<span class="comment">  cvstride - [in] (&gt;=dim+1)</span></div>
<div class="line"><a name="l00439"></a><span class="lineno">  439</span>&#160;<span class="comment">  cv - [in/out]  homogeneous rational control points</span></div>
<div class="line"><a name="l00440"></a><span class="lineno">  440</span>&#160;<span class="comment">  knot - [in/out]</span></div>
<div class="line"><a name="l00441"></a><span class="lineno">  441</span>&#160;<span class="comment">    NURBS curve knots</span></div>
<div class="line"><a name="l00442"></a><span class="lineno">  442</span>&#160;<span class="comment">Returns:</span></div>
<div class="line"><a name="l00443"></a><span class="lineno">  443</span>&#160;<span class="comment">  The cv values are changed so that</span></div>
<div class="line"><a name="l00444"></a><span class="lineno">  444</span>&#160;<span class="comment">  output_bezier(t) = input_bezier(lambda(t)).</span></div>
<div class="line"><a name="l00445"></a><span class="lineno">  445</span>&#160;<span class="comment">See Also:</span></div>
<div class="line"><a name="l00446"></a><span class="lineno">  446</span>&#160;<span class="comment">  ON_ChangeRationalNurbsCurveEndWeights</span></div>
<div class="line"><a name="l00447"></a><span class="lineno">  447</span>&#160;<span class="comment">*/</span></div>
<div class="line"><a name="l00448"></a><span class="lineno">  448</span>&#160;ON_DECL</div>
<div class="line"><a name="l00449"></a><span class="lineno">  449</span>&#160;<span class="keywordtype">bool</span> ON_ReparameterizeRationalNurbsCurve(</div>
<div class="line"><a name="l00450"></a><span class="lineno">  450</span>&#160;          <span class="keywordtype">double</span> c, </div>
<div class="line"><a name="l00451"></a><span class="lineno">  451</span>&#160;          <span class="keywordtype">int</span> dim, </div>
<div class="line"><a name="l00452"></a><span class="lineno">  452</span>&#160;          <span class="keywordtype">int</span> order, </div>
<div class="line"><a name="l00453"></a><span class="lineno">  453</span>&#160;          <span class="keywordtype">int</span> cv_count,</div>
<div class="line"><a name="l00454"></a><span class="lineno">  454</span>&#160;          <span class="keywordtype">int</span> cvstride,</div>
<div class="line"><a name="l00455"></a><span class="lineno">  455</span>&#160;          <span class="keywordtype">double</span>* cv,</div>
<div class="line"><a name="l00456"></a><span class="lineno">  456</span>&#160;          <span class="keywordtype">double</span>* knot</div>
<div class="line"><a name="l00457"></a><span class="lineno">  457</span>&#160;          );</div>
<div class="line"><a name="l00458"></a><span class="lineno">  458</span>&#160; </div>
<div class="line"><a name="l00459"></a><span class="lineno">  459</span>&#160;<span class="comment">/*</span></div>
<div class="line"><a name="l00460"></a><span class="lineno">  460</span>&#160;<span class="comment">Description:</span></div>
<div class="line"><a name="l00461"></a><span class="lineno">  461</span>&#160;<span class="comment">  Use a combination of scaling and reparameterization to set the end</span></div>
<div class="line"><a name="l00462"></a><span class="lineno">  462</span>&#160;<span class="comment">  weights to the specified values.  This </span></div>
<div class="line"><a name="l00463"></a><span class="lineno">  463</span>&#160;<span class="comment">Parameters:</span></div>
<div class="line"><a name="l00464"></a><span class="lineno">  464</span>&#160;<span class="comment">  dim - [in]</span></div>
<div class="line"><a name="l00465"></a><span class="lineno">  465</span>&#160;<span class="comment">  order - [in]</span></div>
<div class="line"><a name="l00466"></a><span class="lineno">  466</span>&#160;<span class="comment">  cvstride - [in] (&gt;=dim+1)</span></div>
<div class="line"><a name="l00467"></a><span class="lineno">  467</span>&#160;<span class="comment">  cv - [in/out] homogeneous rational control points</span></div>
<div class="line"><a name="l00468"></a><span class="lineno">  468</span>&#160;<span class="comment">  knot - [in/out] (output knot vector will be clamped and internal</span></div>
<div class="line"><a name="l00469"></a><span class="lineno">  469</span>&#160;<span class="comment">                   knots may be shifted.)</span></div>
<div class="line"><a name="l00470"></a><span class="lineno">  470</span>&#160;<span class="comment">  w0 - [in]</span></div>
<div class="line"><a name="l00471"></a><span class="lineno">  471</span>&#160;<span class="comment">  w1 - [in]</span></div>
<div class="line"><a name="l00472"></a><span class="lineno">  472</span>&#160;<span class="comment">    The first cv will have weight w0 and the last cv will have weight w1.</span></div>
<div class="line"><a name="l00473"></a><span class="lineno">  473</span>&#160;<span class="comment">    If v0 and v1 are the cv&#39;s input weights, then v0, v1, w0 and w1 must</span></div>
<div class="line"><a name="l00474"></a><span class="lineno">  474</span>&#160;<span class="comment">    all be nonzero, and w0*v0 and w1*v1 must have the same sign.</span></div>
<div class="line"><a name="l00475"></a><span class="lineno">  475</span>&#160;<span class="comment">Returns:</span></div>
<div class="line"><a name="l00476"></a><span class="lineno">  476</span>&#160;<span class="comment">  true if successful</span></div>
<div class="line"><a name="l00477"></a><span class="lineno">  477</span>&#160;<span class="comment">See Also:</span></div>
<div class="line"><a name="l00478"></a><span class="lineno">  478</span>&#160;<span class="comment">  ON_ReparameterizeRationalNurbsCurve</span></div>
<div class="line"><a name="l00479"></a><span class="lineno">  479</span>&#160;<span class="comment">*/</span></div>
<div class="line"><a name="l00480"></a><span class="lineno">  480</span>&#160;ON_DECL</div>
<div class="line"><a name="l00481"></a><span class="lineno">  481</span>&#160;<span class="keywordtype">bool</span> ON_ChangeRationalNurbsCurveEndWeights(</div>
<div class="line"><a name="l00482"></a><span class="lineno">  482</span>&#160;          <span class="keywordtype">int</span> dim, </div>
<div class="line"><a name="l00483"></a><span class="lineno">  483</span>&#160;          <span class="keywordtype">int</span> order, </div>
<div class="line"><a name="l00484"></a><span class="lineno">  484</span>&#160;          <span class="keywordtype">int</span> cv_count,</div>
<div class="line"><a name="l00485"></a><span class="lineno">  485</span>&#160;          <span class="keywordtype">int</span> cvstride, </div>
<div class="line"><a name="l00486"></a><span class="lineno">  486</span>&#160;          <span class="keywordtype">double</span>* cv, </div>
<div class="line"><a name="l00487"></a><span class="lineno">  487</span>&#160;          <span class="keywordtype">double</span>* knot,</div>
<div class="line"><a name="l00488"></a><span class="lineno">  488</span>&#160;          <span class="keywordtype">double</span> w0, </div>
<div class="line"><a name="l00489"></a><span class="lineno">  489</span>&#160;          <span class="keywordtype">double</span> w1</div>
<div class="line"><a name="l00490"></a><span class="lineno">  490</span>&#160;          );</div>
<div class="line"><a name="l00491"></a><span class="lineno">  491</span>&#160; </div>
<div class="line"><a name="l00492"></a><span class="lineno">  492</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="ttc" id="aclass_o_n___text_log_html"><div class="ttname"><a href="class_o_n___text_log.html">ON_TextLog</a></div><div class="ttdef"><b>Definition:</b> opennurbs_textlog.h:23</div></div>
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